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If a charged particle (+q) is projected with certain velocity parallel

June 1, 2025 by rawan239

If a charged particle (+q) is projected with certain velocity parallel to the magnetic field, then it will

trace helical path

trace circular path

continue its motion without any change

come to rest instantly

This question was previously asked in

UPSC NDA-1 – 2015

Download PDF Attempt Online

The correct answer is continue its motion without any change. The magnetic force on a charged particle is given by the Lorentz force formula: F = q(v x B), where q is the charge, v is the velocity vector, and B is the magnetic field vector.

When the velocity vector (v) is parallel to the magnetic field vector (B), the cross product (v x B) is zero. Therefore, the magnetic force (F) on the charged particle is zero. With no force acting on it, the particle will continue to move in a straight line with constant velocity according to Newton’s first law of motion.

A charged particle traces a circular path when its velocity is perpendicular to a uniform magnetic field, and a helical path when its velocity has components both parallel and perpendicular to the field. A magnetic field alone does no work on a charged particle, only changes its direction of motion (unless the velocity is parallel or anti-parallel to the field).

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